TSTP Solution File: SET643+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET643+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:35:01 EDT 2023
% Result : Theorem 0.55s 0.58s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 29
% Syntax : Number of formulae : 42 ( 7 unt; 25 typ; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 36 ( 14 ~; 11 |; 2 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 22 >; 15 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 3 con; 0-3 aty)
% Number of variables : 25 ( 1 sgn; 14 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
set_type: $i ).
tff(decl_23,type,
ilf_type: ( $i * $i ) > $o ).
tff(decl_24,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_25,type,
subset: ( $i * $i ) > $o ).
tff(decl_26,type,
relation_type: ( $i * $i ) > $i ).
tff(decl_27,type,
member: ( $i * $i ) > $o ).
tff(decl_28,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_29,type,
subset_type: $i > $i ).
tff(decl_30,type,
power_set: $i > $i ).
tff(decl_31,type,
member_type: $i > $i ).
tff(decl_32,type,
empty: $i > $o ).
tff(decl_33,type,
relation_like: $i > $o ).
tff(decl_34,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk4_1: $i > $i ).
tff(decl_38,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk7_1: $i > $i ).
tff(decl_41,type,
esk8_1: $i > $i ).
tff(decl_42,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk11_1: $i > $i ).
tff(decl_45,type,
esk12_0: $i ).
tff(decl_46,type,
esk13_0: $i ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( subset(X1,cross_product(X2,X3))
=> ilf_type(X1,relation_type(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(p19,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
fof(p10,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> subset(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
fof(prove_relset_1_5,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ilf_type(cross_product(X1,X2),relation_type(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_5) ).
fof(c_0_4,plain,
! [X6,X7,X8] :
( ~ ilf_type(X6,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X8,set_type)
| ~ subset(X6,cross_product(X7,X8))
| ilf_type(X6,relation_type(X7,X8)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
fof(c_0_5,plain,
! [X59] : ilf_type(X59,set_type),
inference(variable_rename,[status(thm)],[p19]) ).
fof(c_0_6,plain,
! [X35] :
( ~ ilf_type(X35,set_type)
| subset(X35,X35) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p10])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ilf_type(cross_product(X1,X2),relation_type(X1,X2)) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_5]) ).
cnf(c_0_8,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ subset(X1,cross_product(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( subset(X1,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
( ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,set_type)
& ~ ilf_type(cross_product(esk12_0,esk13_0),relation_type(esk12_0,esk13_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_12,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ subset(X1,cross_product(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_9]),c_0_9])]) ).
cnf(c_0_13,plain,
subset(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_9])]) ).
cnf(c_0_14,negated_conjecture,
~ ilf_type(cross_product(esk12_0,esk13_0),relation_type(esk12_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
ilf_type(cross_product(X1,X2),relation_type(X1,X2)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12 % Problem : SET643+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 10:32:50 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 0.55/0.58 % Version : CSE_E---1.5
% 0.55/0.58 % Problem : theBenchmark.p
% 0.55/0.58 % Proof found
% 0.55/0.58 % SZS status Theorem for theBenchmark.p
% 0.55/0.58 % SZS output start Proof
% See solution above
% 0.55/0.59 % Total time : 0.007000 s
% 0.55/0.59 % SZS output end Proof
% 0.55/0.59 % Total time : 0.010000 s
%------------------------------------------------------------------------------